Inflationary Effect of Interest Rate Policy: Exchange Rate Pass-Through to Inflation

By Juhyeon Eom.

The past couple of decades are marked by astonishing macroeconomic success in delivering unprecedented price stability. Indeed, humanity has never observed such a combination of a consistently low rate of inflation and unemployment for an extended period — many have celebrated this massive triumph in macroeconomic doctrine. While the horror of inflation gradually faded, a sudden burst in inflation in 2022 has baffled both the public and many economists neither of whom have foreseen a revival of the inflationary burst. Now inflation rate in the UK peaked at 10.1% in July 2022, a few tenth percentage points shy from the record since the 1970s, a decade plagued by a consistently high rate of inflation (Office of National Statistics).

Why does this inflationary surge matter? We are in a pivotal moment that will shape the macroeconomic circumstances for the next few years or even for decades to be unfolded. The same logic of a consistently low rate of inflation in the post-2008 economy applies to the inflationary economy to come where drifting and re-anchoring inflationary expectations may linger afterwards. Or perhaps we may need to introduce a round of painful Volcker-type hawkish austerity to flatten the Philips curve.

The misdiagnosis of the nature of the current inflationary episode lies at the heart of the cause of what we are seeing today. Mistakenly having a faith in fully anchored inflationary expectation and their diagnosis of the temporal nature of inflation driven by supply-side disruptions, central banks were complacent with their price stability mandate and failed to rein inflationary surge in the incipient phase (Reis 2022).

This is the reason why it is important to have a clear picture of the nature of inflation. The clearer vision we have, the better we respond. In this paper, I will discuss the exchange rate channel through which macroeconomic ramifications of monetary policy are delivered. The analytical framework is adopted from the real interest differential theory of exchange rate determination developed in Frankel’s paper “On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differential”.

I. The Real Interest Differential Theory of Exchange Rate Determination

As representative explanatory models of the relationship between interest rates and exchange rates, I choose Frenkel’s real interest differential theory of exchange rate determination and its variations depending on prevailing assumptions on price rigidities in the economy as proposed in his paper “On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differential” (Frankel 1979). The empirical justification of the model’s explanatory power is mixed. While some prominent literature noted that the interest differential theory of exchange rate determination performed any better than the random walk theory (Meese and Rogoff 1983), the vindication has been written as of recently — marked by notable empirical successes and garnered support for the model’s usefulness (Engel, Charles, and West 2005).

The theory starts with two fundamental assumptions. First, interest rate parity is associated with the forward rate of currency given the perfect substitutability of the bonds of different countries:

where r is defined as one plus the domestic rate of interest in the logarithmic scale and r* is defined as one plus the foreign rate of interest in the logarithmic scale. Given that d denotes the forward discount (or expected depreciation), defined as the log of the forward rate minus the log of the current spot rate, then d is equal to interest parity or interest differential between two countries under perfect capital mobility. In the absence of transaction costs, interest parity theory states that equilibrium for a forward discount or premium rate is established whereby no covered arbitrage is profitable. (Frenkel and Levich 1975). Failing to reach such equilibrium implies unexploited opportunities for certain profits, whereas the profitable and riskless arbitrage between perfectly substitutable assets can be made in the frictionless economy if the return differential deviates from the expected forward exchange rate. Furthermore, empirical data substantiate that interest parity is consistently smaller than actual transaction costs in the economy (Frenkel and Levich 1975).

The second fundamental assumption is that the forward discount rate is a function of the gap between current and equilibrium spot rates, as denoted by bar e and e, respectively, and of the long-run inflation differential between the domestic and foreign countries:

where variables denoting spot rates and long-run inflation are all in a logarithmic scale. Meantime, the long-term inflation differential, pi — pi*, is unobservable and therefore the proxies are constructed from variables that are considered an approximate rate of monetary growth in the economy — such as long-term interest rate differentials. The estimation measure that is frequently used in the relevant literature is government long-term bond rates (Frankel 1981; Hooper and Morton 1982; Rogoff 1982).

In the short run, the spot rate may deviate from its equilibrium rate, e bar, so that d decreases at a rate which is proportional to the current gap in the exchange rate. That is, so long as e — e bar is greater than zero, the forward rate converges and therefore exchange rate is expected to return to its equilibrium value. In the long run, where e = e bar, it is expected to change at the long-run rate of inflation pi — pi*. This long-run relationship between exchange rate and long-run inflation differential is substantiated by the assumption of purchasing power parity, that real exchange rates tend toward purchasing power parity in the very long run (Rogoff 1996). That is, the positive inflation differential in the domestic economy results in a positive forward discount or expected depreciation as per the Law of One Price, which requires that:

where sum P_i denotes the overall price level in the economy, where E denotes the exchange rate, and t subscripts denote time (Rogoff 1996). ZCombining equations (1) and (2) gives

As per the definition, r — pi refers to the real interest rate and the expression in brackets refers to the real interest differential. Note that in the long run, where e = e bar, we must have r bar — r* bar = pi — pi*, where r bar and r* bar denote the long-run, short run interest rates. Two prevailing explanations ensure r bar — r* bar = pi — pi* in the long run (Frankel 1979). First, the long-run equality between interest and inflation rate differential follows from the interest rate parity of equation (1) stating equality of the interest rate differential and expected depreciation and from the long-run relative purchasing power parity of equation (2) stating long-run equality between inflation rate differential and expected depreciation. Alternatively, given the perfect substitutability and perfect mobility of capital, international investment flows lead to real interest rates equality across borders: r bar — r* bar = pi — pi*. That is, given the aforementioned assumptions hold, investment flows from a low-interest country to a high-interest country and thus balances the long-run interest rate between the two countries.

In the long run where e = e bar, the purchasing power parity gives another equation of exchange rate:

where p bar and p* bar are defined as equilibrium price levels at the domestic and foreign economy in a logarithmic scale, respectively (see above for the Law of One Price requires this equation to be true). However, this assumption is untenable in the real market economy that departs from the Law of One Price for international trade even within categories of closed related goods (Kravis and Lipsey 1977; Rogoff 1996). Whereas this assumption provides this model with an analytical framework and power by providing essentially a one-good model that relates explanatory variables with the dependent variable (i.e., equilibrium exchange rate) as we shall see below.

Assume a conventional money demand equation:

where m, p and y are defined as the domestic money supply, price level, and output in a logarithmic scale (Frankel 1979). If we take the difference between the money supply at home and abroad, denoted by m and m*, respectively, we obtain equation (6) below.

Using bars to denote equilibrium values and from equation (4) and long-run equality bar r — bar r* = pi — pi* when e = e bar, we obtain

S

This equation illustrates the monetary theory of the exchange rate, according to which the exchange rate is determined by the explanatory variables above. Intuitively, when money supply accelerates against foreign money supply, it will inflate prices and thus raises the exchange rate proportionately, and an increase in income or a decrease in the expected rate of inflation against the foreign economy results in an increase in demand for money and thereby lowering the exchange rate.

Substituting (7) into (3), and assuming that the equilibrium money supplies and income levels are given by their current actual levels, we obtain a complete equation of spot rate of determination:

Though the above assumption that equilibrium money supplies and income levels are equal to their current actual levels does not necessarily hold an extension study without the assumption is also viable, such assumption here confers the model merit of brevity.

II. Two hypotheses

Equation (8) is reproduced here with an error term u

where alpha =-1 / theta and beta = 1 /theta + lambda and beta is always greater than alpha in an absolute term. In the original paper, Frankel discusses the two conflicting hypotheses: the Chicago theory of exchange rate model attributable to Frenkel and Bilson and the Keynesian approach from Dornbusch.

Chicago theory assumes perfect flexibility in price, and as a consequence of such assumption, changes in the nominal interest rate are more or less the result of changes in the expected inflation rate.[1] Therefore, a rise in inflation coincides with a rise in the nominal interest rate and a fall in demand for domestic currency since both signify the reduction in the relative value of the domestic currency due to inflation. The exchange rate, defined as the price of foreign currency, rises as the domestic currency depreciates instantly. This line of thought originated from Chicago tradition states that there is a positive relationship between the exchange rate and the nominal interest rate differential (Frankel 1979). Another remark on Chicago’s theory explains an extremely important feature in the exchange rate model built upon Chicago’s theoretical setting. As per the reason above, we can no longer claim the exogeneity of inflation and interest rate differential variables. This is highlighted by the Bilson-Frenkel model where Bilson assumes alpha > 0 and beta = 0 and Frenkel assumes alpha = 0 and beta > 0.

An alternative model is proposed by Dornbusch who takes a Keynesian approach (Dornbusch 1976). Unlike Chicago theory, Dornbusch’s model assumes price stickiness, at least in the short run, and therefore beta is automatically fixed to zero. When the domestic interest rate rises relative to the foreign rate, it is largely attributable to the monetary expansion, following the casual Marshallian demand and supply analysis in the money market. Another characteristic feature of Dornbusch’s model is that the asset view is centred on his explanation of exchange rate dynamics. The higher interest rate at home attracts a capital inflow, thereby appreciating domestic currency against foreign currency. Therefore, we have a negative relationship between the exchange rate and the nominal interest rate differential with alpha < 0.

In light of the current economic situation, Dornbusch’s explanatory model stands as a more convincing case. According to Frankel, when the variation in inflation differential is small, Dornbusch’s model provides a more realistic description, and the opposite is true for the Chicago theory.[2] In the original paper, Frankel proposes and develops a model that is tailored for moderate variations in inflation differential in the 1970s. With reference to Frankel’s yardstick of small variation, namely the Canadian float against the United States in the 1950s where the inflation rate diverged no more than 4%, Dornbusch’s model seems to be the best fit for the study of the US-UK case in the late 2010s to early 2020s (Schembri 2008).

The final model in the use is as below, with each coefficient replaced with

III. Data

To obtain an estimation model, regression was run based on the equation above. Specifically, OLS multivariate regression technique is used. Then, I will expedite and estimate the extent to which the current monetary regime has incurred an inflationary effect by extrapolating from the illustrative model. Formally, we solve the optimisation problem of the least square below with the omission of the error term:

­One drawback to this approach is that it is hard to address the statistical issues that arise from its exogeneity assumption; that is the dependent variables in the theoretical model should not be treated as exogenous variables. Instead, they are more realistically thought of as endogenous variables. The possibility that the explanatory variables in the above equation are endogenous is shown by Meese and Rogoff (1983). For instance, short-term interest differential is generally endogenous where the value is correlated with income differential. Yet in this article, these variables are still treated as legitimate regressors in the multivariable regression model.

This statistical issue remains unaddressed in this article and this error is especially critical in this methodological setting. But this statistical issue does not severely diminish the predictive power of the exchange rate model per se when an appropriate statistical apparatus is complemented. For instance, many prominent works took the autoregression method that takes error term into the equation working as a mitigating factor to erroneous endogeneity of the explanatory variable [see Frankel (1979), Hooper and Morton (1982), and Meese and Rogoff (1983)].

The data are from Office for National Statistics (the UK) and FRED Economics Data: St. Louis FED (the US) and are presented in Table 1 below:

Before presenting the results of the regression tests, we need to explain the rationale for each regression test and most importantly the regression with the coefficient on the relative money supply has been set to 1.0 (that is, beta_1 = 1) as Frankel postulated on his paper based on empirical data. The regression test on original data determines the coefficients of three variables in a way that maximizes the explanatory power of these three variables within the time of the investigation — referred to as the “best-fit” model. Indeed, the extent of deviation from the actual exchange rate to the estimate measured by the R-squared method indicates the superiority of the “best-fit” estimate to the second estimate in explaining the locus of real exchange rate fluctuation[3]. Nonetheless, beta_2 and beta_3 have the t-statistics of 1.64 and 1.54, indicating that these are statistically significant at 5% significance level, so we do not reject it at 5% significance level, from which we cannot hastily disqualify the second model if the model could provide more convincing rationales. The extent of the deviation, if not substantial, is not a single consideration when evaluating a quantitative model that tries to explain reality. Even though the predictive model provides some reasonable trace of the movement within the limited scope of the study (3-year range in this case), we cannot extrapolate them entirely to claim the predictive power of the model if one does not reflect the theory underlies the model. In light of the argument, Frankel proposed in his paper that the coefficient of the relative money supply is insignificantly less than 1.0 ­– the value deviates from the narrow range so that it conforms with his general theory of explanation.

Thus, table 2 shows the results of the multivariate OLS regression from 1) original data and 2) the coefficient on the relative money supply has been set to 1.0. The estimated equations given from OLS are:

The first model does not conform with Dornbusch’s hypothesis that the coefficient of the short-term interest rate differential term should be negative. That is, the asset approach taken by Dornbusch built upon the basic tenets of the Keynesian hypothesis no longer explains the estimated model. The “best-fit” estimate thus objects to the hypothesis that seemed most probable in the current setting of the monetary regime [as discussed in section II]. Also, Frankel proposed that the coefficient of relative production is significantly negative and is estimated at the range of –.5 which suits the interpretation of the elasticity of money demand with respect to income. The “best-fit” estimate does not conform with either Dornbusch’s or Frankel’s hypothesis of exchange rate determination.

While our second model seems to provide a sounder interpretation of reality, the extent of deviation seems to be more substantial than it appears in the R-squared value. Especially, as shown in figure 1, the model is unable to accommodate the unexpected shock in the variables as exemplified by a stark deviation from May 2020 to June 2020 followed by a sudden spike in the relative money supply. Moreover, from time to time, the model implies the opposite direction of the dynamic development trajectory of the exchange rate which makes it harder to reconcile the predictive model to the real economy. Both instances hint at the erroneous gauge of the coefficients or even the omission of other decisive factors in play.

The regression results do not provide an entirely satisfactory model. Indeed, both estimates are subject to some error. However, it is confirmed that the coefficient of the relative interest rate is significantly positive in both models — which suffices our purpose of the study to investigate the implication of interest rate policy to the economy.

IV. Findings

In this section inflationary effect of interest policy through the channel of exchange rate variation is discussed. Multiple studies on macroeconomic implications of variations in exchange rates shed light on the “remarkably robust” relationship between commodity prices and exchange rates, that the commodity prices are exogenous to the exchange rates (Chen, Rogoff, and Rossi 2010; Kohlscheen et al. 2016). For the merit of brevity, we assume here that the percentage change in the exchange rate results in a proportionate change in commodity prices, that is delta log (e) = delta log (commodity prices). This assumption, nonetheless, is likely to be a conservative measure of the magnitude of change since it only accounts for the direct impact of exchange rate variations as the US dollar is used as a means of international transaction. The exchange rate transmission channel is pertinent to understanding current economic complications in the United Kingdom associated with a combination of high inflation and subsequent costs of living crisis — which coincided with prescriptive interest rate policies by the Bank of England.

From the explanatory model we developed in section III, we notice that the coefficient for relative interest rate is significantly positive at the range of 0.028 to 0.1525. That is, a single percentage increment of the US base interest rate depreciates the UK pound sterling against the US dollar by 0.028 to 0.1525 units depending on the model we devise. The hawkish interest rate policy by the US Federal Reserve that raised 425 percentage points from the zero bound within 2 years and 6 months from March 2020 had a pernicious effect on cost-push inflation in the UK, aggravating the cost-of-living crisis in the UK. By our simplistic model, the US’s interest rate policy alone is responsible for a 2.15 % to 11.73% rise in imported commodity prices. Comparing this value to the magnitude of producer price inflation, which peaked at a 20.8% annual rate in September 2022, the implication of the US interest rate policy is certainly inflationary and does seem profound. However, the interest rate policy by the Bank of England, throughout our investigation period, worked in tandem with the Federal Reserve in combat against inflationary surges. The interest differential weighed in favour of the British Pound against the US dollar in our estimate, especially on the verge of supply-side strains during the incipient stage of the Russian invasion of Ukraine where the interest rate is 1.00 percentage higher in the UK.

The major caveat to the study is that the risk appetite in the financial market has shifted dramatically over the course of events and the respective impact which interest rate differential has on exchange rate, viz., it invalidates the use of the uniform predictive model to determine the exchange rate in 2019 and the exchange rate in 2022. Especially, the motive for seeking safer assets predominates the economy after the commencement of the Russian invasion given the highly uncertain future economic prospect due to the escalation of geopolitical tensions and general retreat in globalization and the subsequent deterioration in business prospects. Therefore, the series of radical shifts in the economy have impacted the error variable (epsilon_e) which lies beyond the scope of the above econometric analysis.

Indeed, a general fall in British Pound to the US dollar may be largely attributed to the change in risk appetite in the financial market and the subsequent speculative movements in the FX market. In the face of the shift, interest rate policy by the Bank of England has failed to secure their exchange rate to the historical standard — a more hawkish approach by the Bank of England should have sufficed the risk premium and put a cease to the exodus in the financial market. In such a way, the interest rate has been inflationary through the exchange rate channel, however, this lies beyond the scope of our study and could potentially be an extension to further refine our understanding of the phenomenon.

V. Concluding Remarks

The paper is motivated to gauge the extent to which the interest rate policy influences the exchange rate and through which channel the inflationary effect of interest rate policy may be delivered. The model developed in this paper is adequate to establish the general implications of interest rate policy on domestic inflation. However, there is a scope for improvement in our model and analysis to better appreciate the extent to which the interest rate policies by the Bank of England and the Federal Reserve are responsible for the current supply-side-led inflation in the United Kingdom, as discussed in section IV. Such is where the frontier of economic research could bring us.

REFERENCES

Chen, Y.C., Rogoff, K.S. and Rossi, B. 2010 “Can Exchange Rates Forecast Commodity Prices,” Quarterly Journal of Economics, pp. 1145–1194.

Dornbusch, R., 1976. “Expectations and Exchange Rate Dynamics,” Journal of Political Economy, 84, 1161–76.

Engel, Charles, and Kenneth D. West. 2005. “Exchange Rate and fundamentals.” Journal of Political Economy 113, 485–517.

Frankel, J. A. 1979. On the Mark: A Theory of Floating Exchange Rates Based on Real Interest Differentials. The American Economic Review, 69(4), 610–622.

Frenkel, J. A., and Levich, R. M. 1975. Covered Interest Arbitrage: Unexploited Profits? Journal of Political Economy, 83(2), 325–338.

Kohlscheen, Emanuel, Avalos, F. H. and Schrimpf, Andreas. 2016 “BIS Working Paper: When the Walk is not Random: Commodity Prices and Exchange Rates”, Bank for International Settlements

Kravis, I. B., and Lipsey, R. E. 1977. Export Prices and the Transmission of Inflation. The American Economic Review, 67(1), 155–163.

Hooper, Peter, and Morton, John. 1982. Fluctuations in the dollar: A model of nominal and real exchange rate determination, Journal of International Money and Finance, Elsevier, vol. 1(1), pages 39–56, January.

Meese, Richard, and Rogoff, Kenneth. 1983. Empirical Exchange Rate Models of the Seventies: Do They Fit Out of Sample? Journal of International Economics 14: 3–24.

Reis, Ricardo 2022, “DP17514 The Burst of High Inflation in 2021–22: How and Why Did We Get Here?”, CEPR Press Discussion Paper №17514.

Rogoff, Kenneth. 1996. The Purchasing Power Parity Puzzle. Journal of Economic Literature, 34(2), 647–668.

Schembri, L. 2008 “Canada’s Experience with a Flexible Exchange Rate in the 1950s: Valuable Lessons Learned,” Bank of Canada Review, 3–15

[1] A rise in the domestic interest rate relative to the foreign interest rate is because the domestic currency is losing value against foreign currency through inflation.

[2] According to Frankel (1979), the Chicago theory provides an accurate description of when variation in inflation differential is large, as in the hyperinflation in Germany in 1920. Meantime, he proposes the Canadian float against the United States in the 1950s as an instance where Dornbusch’s model is deemed an appropriate fit.

[3] The point is self-evident in the mechanism of computing OLS regression that minimizes the sum of residuals.